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Proving Triangle Congruence Using ASA and AAS Methods

In this lesson, we will explore how to prove triangles congruent using the Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates. We will summarize various triangle congruence methods and engage in exercises to enhance understanding. By working through homework questions and completing tables, you will identify key congruence criteria such as SAS (Side-Angle-Side) and HL (Hypotenuse-Leg) while applying geometric theorems. Get ready to solidify your understanding of triangle congruence!

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Proving Triangle Congruence Using ASA and AAS Methods

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  1. 4.5.2 Prove Triangles Congruent by ASA and AAS Chapter 4: Congruent Triangles SWBAT: Summarize Triangle congruence postulates and theorems. You will accomplish this by answering questions on homework and filling in the table on slide 2

  2. Triangle Congruence Postulates and Theorems • Name the 5 methods we have discussed • Right triangle congruencies: Check P. 252

  3. Name the theorem: SAS • Proof: • CB  AD (Given) • BC || AD • ACB  CAD (AIA thm) • CA  AC (Symmetric Property) • Then •  ABC   CDA by SAS B C A D

  4. Fill in the necessary information: • Given  CB  CD, ED  EB, CB  ED, ____ _____ • Prove: CBD   EDB by HL E B F A C D

  5. Fill in the necessary information: • Given  AB  FD, EF  CA, ____ _____ • Prove: ABC   FDE by SSS E B F A C D

  6. Homework • P. 253 • 2, 7, 10, 20, 22, 31, 33

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